Related papers: Wasserstein Barycenter Model Ensembling
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability…
As interest in graph data has grown in recent years, the computation of various geometric tools has become essential. In some area such as mesh processing, they often rely on the computation of geodesics and shortest paths in discretized…
Wasserstein barycenters and variance-like criteria based on the Wasserstein distance are used in many problems to analyze the homogeneity of collections of distributions and structural relationships between the observations. We propose the…
Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing…
Active learning has emerged as a standard paradigm in areas with scarcity of labeled training data, such as in the medical domain. Language models have emerged as the prevalent choice of several natural language tasks due to the performance…
A robust clustering method for probabilities in Wasserstein space is introduced. This new "trimmed $k$-barycenters" approach relies on recent results on barycenters in Wasserstein space that allow intensive computation, as required by…
Semantic segmentation is important for many real-world systems, e.g., autonomous vehicles, which predict the class of each pixel. Recently, deep networks achieved significant progress w.r.t. the mean Intersection-over Union (mIoU) with the…
Consider a multi-agent system whereby each agent has an initial probability measure. In this paper, we propose a distributed algorithm based upon stochastic, asynchronous and pairwise exchange of information and displacement interpolation…
In this article, we study Wasserstein-type metrics and corresponding barycenters for mixtures of a chosen subset of probability measures called atoms hereafter. In particular, this works extends what was proposed by Delon and Desolneux [A…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
Learning generative models is challenging for a network edge node with limited data and computing power. Since tasks in similar environments share model similarity, it is plausible to leverage pre-trained generative models from the cloud or…
Disentangling polysemantic neurons is at the core of many current approaches to interpretability of large language models. Here we attempt to study how disentanglement can be used to understand performance, particularly under weight…
We propose the linear barycentric coding model (LBCM) which utilizes the linear optimal transport (LOT) metric for analysis and synthesis of probability measures. We provide a closed-form solution to the variational problem characterizing…
This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic means after finding the optimal transport plans between the…
We introduce a weak notion of barycenter of a probability measure $\mu$ on a metric measure space $(X, d, {\bf m})$, with the metric $d$ and reference measure ${\bf m}$. Under the assumption that optimal transport plans are given by…
This paper targets the task with discrete and periodic class labels ($e.g.,$ pose/orientation estimation) in the context of deep learning. The commonly used cross-entropy or regression loss is not well matched to this problem as they ignore…
The consensus problem -- achieving agreement among a network of agents -- is a central theme in both theory and applications. Recently, this problem has been extended from Euclidean spaces to the space of probability measures, where the…
In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…